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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 155a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
155.a2 | 155a1 | \([0, -1, 1, 10, 6]\) | \(99897344/96875\) | \(-96875\) | \([5]\) | \(20\) | \(-0.35618\) | \(\Gamma_0(N)\)-optimal |
155.a1 | 155a2 | \([0, -1, 1, -840, -9114]\) | \(-65626385453056/143145755\) | \(-143145755\) | \([]\) | \(100\) | \(0.44854\) |
Rank
sage: E.rank()
The elliptic curves in class 155a have rank \(1\).
Complex multiplication
The elliptic curves in class 155a do not have complex multiplication.Modular form 155.2.a.a
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.